300 research outputs found
Metastable legged-robot locomotion
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-215).A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.by Katie Byl.Ph.D
Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem
Given a submersion with an Ehresmann connection ,
we describe how to solve Hamiltonian systems on by lifting our problem to
. Furthermore, we show that all solutions of these lifted Hamiltonian
systems can be described using the original Hamiltonian vector field on
along with a generalization of the magnetic force. This generalized force is
described using the curvature of along with a new form of
parallel transport of covectors vanishing on . Using the
Pontryagin maximum principle, we apply this theory to optimal control problems
and to get results on normal and abnormal extremals. We give a
demonstration of our theory by considering the optimal control problem of one
Riemannian manifold rolling on another without twisting or slipping along
curves of minimal length.Comment: 31 page
Topology based representations for motion synthesis and planning
Robot motion can be described in several alternative representations, including
joint configuration or end-effector spaces. These representations are often used for
manipulation or navigation tasks but they are not suitable for tasks that involve
close interaction with the environment. In these scenarios, collisions and relative
poses of the robot and its surroundings create a complex planning space. To deal
with this complexity, we exploit several representations that capture the state of
the interaction, rather than the state of the robot. Borrowing notions of topology invariances
and homotopy classes, we design task spaces based on winding numbers
and writhe for synthesizing winding motion, and electro-static fields for planning
reaching and grasping motion. Our experiments show that these representations
capture the motion, preserving its qualitative properties, while generalising over
finer geometrical detail. Based on the same motivation, we utilise a scale and
rotation invariant representation for locally preserving distances, called interaction
mesh. The interaction mesh allows for transferring motion between robots of
different scales (motion re-targeting), between humans and robots (teleoperation)
and between different environments (motion adaptation). To estimate the state of
the environment we employ real-time sensing techniques utilizing dense stereo
tracking, magnetic tracking sensors and inertia measurements units.
We combine and exploit these representations for synthesis and generalization
of motion in dynamic environments. The benefit of this method is on problems
where direct planning in joint space is extremely hard whereas local optimal control
exploiting topology and metric of these novel representations can efficiently
compute optimal trajectories. We formulate this approach in the framework of
optimal control as an approximate inference problem. This allows for consistent
combination of multiple task spaces (e.g. end-effector, joint space and the abstract
task spaces we investigate in this thesis).
Motion generalization to novel situations and kinematics is similarly performed
by projecting motion from abstract representations to joint configuration space.
This technique, based on operational space control, allows us to adapt the motion
in real time. This process of real-time re-mapping generates robust motion, thus
reducing the amount of re-planning.We have implemented our approach as a part
of an open source project called the Extensible Optimisation library (EXOTica).
This software allows for defining motion synthesis problems by combining task
representations and presenting this problem to various motion planners using a
common interface. Using EXOTica, we perform comparisons between different
representations and different planners to validate that these representations truly
improve the motion planning
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